% Source: ACM ICPC World Finals 2000, problem D

\begin{problem}{Gifts Large and Small}{gifts.in}{gifts.out}{1 second}{64 megabytes}

WrapIt.com specializes in wrapping gifts. Started several years ago as a service offered to local department stores
and malls, today WrapIt serves customers world-wide and boasts that it can package anything from half-carat
diamonds to whole apartment blocks.
WrapIt has found that some customers prefer their gifts to be wrapped in the smallest possible packages, whereas
others prefer large packages that make their gifts seem larger than they really are. The company needs a program
that computes the smallest and largest rectangular package into which a gift can be ?tightly? wrapped. Since this is a
difficult problem, the company will initially settle for a two-dimensional version of the program.
Each gift is approximated as a simple polygon, and all packages are represented by rectangles. A gift is said to ?fit
tightly? in a package if the gift touches all four sides of the package. The figure below shows how a triangular gift
might fit tightly in two packages of different sizes. For each gift, your program must compute the areas of the
smallest and largest packages into which the gift can fit tightly.

\InputFile

The input contains several gift descriptions. Each description begins with a line containing an integer n
($3 \le n \le 100$), which is the number of vertices in the polygon that represents the gift. The following n lines contain
pairs of integers that represent the coordinates of the polygon vertices, in clockwise order. Each polygon will have a
non-zero area and will not intersect itself.
The input is terminated by a line containing the integer $0$.

\OutputFile

For each gift, first print the number of the gift. Then on separate lines, print the minimum and maximum areas of the
packages into which the gift fits tightly, using the format in the sample output. Print a blank line after each test case.
The computed areas should be exact to three digits to the right of the decimal point.

\Example

\begin{example}
\exmp{
3
-3 5
7 9
17 5
4
10 10
10 20
20 20
20 10
0
}{%
Gift 1
Minimum area = 80.000
Maximum area = 200.000

Gift 2
Minimum area = 100.000
Maximum area = 200.000
}%
\end{example}

\end{problem}
